Speaking on ITV News during a visit to Malaysia, Warsi said: “I take these allegations very seriously. It’s why I said right at the outset that I would fully co-operate with any investigation. I believe that being a member of the House of Lords is a privilege. I take that privilege seriously.

“It’s why I have always ensured that my conduct, including in relation to expenses and allowances, is both in accordance with the law and the spirit of the rules.”

Warsi declined to answer questions on whether she will stand down pending the inquiry. But she has so far received strong public backing from Conservative party officials and MPs.

John Mann, the Labour MP for Bassetlaw, had called for the issue to be investigated by the parliamentary commissioner for standards.

Such inquiries can often take months and could overlap with an expected summer reshuffle, where she has been widely tipped to be moved to a less high-profile role.

The inquiry will have to examine the relative lax allowances regime in the Lords at the time she made the claims in 2008. It will also have to look at whether, as she claims, she paid rent to a special adviser who was then supposed to give the money to the landlord.

Warsi has said she made expenses claims because she sometimes spent nights in a London hotel.